The proofs of the standard CLR inequality for Schrödinger operators on \(\mathbb {R}^n\) , \(n\ge 3\) , uses the fact that for the Laplacian on \(\mathbb {R}^n\)  with \(n\ge 3\)  the essential spectrum contains 0 and the resolvent \((\Delta -\lambda )^{-1}\)  has a weak limit as \(\lambda \rightarrow 0^{-}\) . This allows us to take \(\lambda =0\)  in (REF ) and get an upper bound for \(N^{-}(H_{V})\)  (see [1]}).
